I am creating a banner 960x320 px in Indesing. When I export as JPEG and load in to the website it show very bigger. I have opened the JPEG in Photoshop and checked the Pixel in Image size panel it is showing 2333 x 778.

Pixels have no physical size. If you have a 960 × 320 pixel image in Photoshop then that is the size in pixels, regardless of the PPI value in the file. InDesign files don’t work in pixels. They have a unit the program calls pixels, but that is misnamed because, since everything in InDesign has a physical size, so do those pixels. Those pixels are 1/72 of an inch. Draw a one inch square in InDesign then switch to pixels. The square is reported as being 72 pixels. If you want that share to be saved as a 72 pixel raster image you need to export at 72 pixels per inch. You didn’t do that. You exported at 175 pixels per inch. You see that square you thought you said should be 72 pixels isn't any more, now it’s 350 pixels.

TL;DR: Export at 72 PPI or save a PDF and rasterize in Photoshop at 72 PPI.

When you create the images from Indesign, the image size is change in accordance to the output setting of image (It goes larger or smaller).. It doesn't define and go according to the document size of indesign.

So, If you want the images of indesign in Photoshop than create the new document size (960px 320px) in Photoshop and place the export indesign image.

This is the only to do it... and you will get it what you are wanted for.

And if you one the exact image size that you have created in Indesign than export to jpeg and do the setting of Image: Resolution (ppi) as 72 and Color space as RGB than this will get it to the exact point.....